Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study

Abstract

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector Quantum Monte Carlo (QMC) method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction-dependence of the Z2 topological insulator/trivial insulator phase boundary by calculating the Z2 invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum °uctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.

References in corpus (37)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Mott physics and band topology in materials with strong spin-orbit interaction
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Single particle Green's functions and interacting topological insulators
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Evidence for electron-electron interaction in topological insulator thin films
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two dimensional limit
• Simplified topological invariants for interacting insulators
• Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Fractional topological insulators in three dimensions
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy
• Correlated Topological Insulators and the Fractional Magnetoelectric Effect
• Interaction effects and quantum phase transitions in topological insulators
• Correlation effects on 3D topological phases: from bulk to boundary
• Competing Exotic Topological Insulator Phases in Transition Metal Oxides on the Pyrochlore Lattice with Distortion
• Topological phases and phase transitions on the square-octagon lattice
• Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator
• Topological invariants for interacting topological insulators with inversion symmetry
• Topological Phase Transitions for Interacting Finite Systems
• Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
• A study on correlation effects in two dimensional topological insulators
• Interaction induced topological phase transition in Bernevig-Hughes-Zhang model
• Pole expansion of self-energy and interaction effect on topological insulators
• Frequency domain winding number and interaction effect on topological insulators
• Properties of A Class of Topological Phase Transition

Cited by in corpus (48)

• Interacting topological insulators: a review
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Rashba spin orbit coupling in the Kane-Mele-Hubbard model
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown
• Edge states in graphene-like systems
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Insensitivity of bulk properties to the twisted boundary condition
• First order topological phase transition of the Haldane--Hubbard model
• Z2 topological invariants in two dimensions from quantum Monte Carlo
• Strong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
• Magnetic Order Driven Topological Transition in the Haldane-Hubbard Model
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
• Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons
• Ab initio study of $Z_2$ topological phases in perovskite (111) $({\text{SrTiO}}_3{)}_7/({\text{SrIrO}}_3{)}_2$ and $({\text{KTaO}}_3{)}_7/({\text{KPtO}}_3{)}_2$ multilayers
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Correlation effects in pyrochlore iridate thin films grown along the $[111]$ direction
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Topological Phase Transition in the Hofstadter-Hubbard Model
• Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Disorder effects in correlated topological insulators
• Triplet $p+ip$ paring correlation in doped Kane-Mele-Hubbard model: A quantum Monte Carlo study
• Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Analytical approach for the Mott transition in the Kane-Mele-Hubbard model
• Braiding of edge states in narrow zigzag graphene nanoribbons: effect of the third neighbors hopping
• Quantum phase transitions of topological insulators without gap closing
• Effects of short-ranged interactions on the Kane-Mele model without discrete particle-hole symmetry
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Short-ranged interaction effects on $Z_2$ topological phase transitions
• Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
• Quasiparticle picture of topological phase transitions induced by interactions
• Phase transitions of the Kane-Mele-Hubbard model with a long-range hopping
• Multitude of phases in correlated lattice fermion systems with spin-dependent disorder
• Real-space topology and charge order in the Haldane-Holstein Model
• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
• Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method